PAGEOPH, Vol. 133, No. 3 (1990) 0033-4553/90/030489-3351.50 + 0.20/0 9 1990 Birkh/iuser Verlag, Basel The Damage Mechanics of Brittle Solids in Compression M. F. ASHBY ~ and C. G. SAMMIS 2 Abstract--The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data. Key words: Damage mechanics, brittle fracture, microcracks, fracture mechanics, rock mechanics, fracture nucleation, crack growth. I. Introduction When a brittle solid is loaded to failure, it does so by the propagation of cracks. The cracks nucleate and propagate from inhomogeneities, by which we mean holes, inclusions, microcracks, surface scratches or other defects. The difference between compressive and tensile fracture is that in tension a single crack grows unstably (once started, it accelerates across the sample to cause failure) while in compression a population of small cracks extends stably, each growing longer as the stress is raised, until they interact in some cooperative way to give final failure (Figure 1). Because of this, the strength of a brittle solid in compression is usually greater, by a factor of ten or more, than that in tension. Measurements of the crushing strength of stone, brick and of cement must have been of interest to civil engineers since pre-Roman times. Systematic measurements of compressive strength really began about the middle of the last century (for its history, see JAEGER and COOK, 1976) but without much attempt to understand what determined it, or why brittle materials had useful strength in compression but none to speak of in tension. Elucidation of the mechanics of brittle tensile fracture 1Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 IPZ, England. 2 Department of Geological Sciences, University of Southern California, University Park, California 90089-0740, U.S.A.